Controllers for regulated power inverters, AC/DC, and DC/DC converters

ABSTRACT

Methods and corresponding apparatus for regulation, control, and management of DC-to-AC, AC-to-DC, and/or DC-to-DC switching power conversion.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/961,147 (filed on Apr. 24, 2018), which is a continuation-in-part ofU.S. patent application Ser. No. 15/803,471, filed 3 Nov. 2017 (now U.S.Pat. No. 9,985,515), which is a continuation-in-part of U.S. patentapplication Ser. No. 15/646,692, filed 11 Jul. 2017 (now U.S. Pat. No.9,843,271). This application is also related to the U.S. provisionalpatent applications 62/362,764 (filed on 15 Jul. 2016) and 62/510,990(filed on 25 May 2017), which are incorporated therein by reference intheir entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

None.

COPYRIGHT NOTIFICATION

Portions of this patent application contain materials that are subjectto copyright protection. The copyright owner has no objection to thefacsimile reproduction by anyone of the patent document or the patentdisclosure, as it appears in the Patent and Trademark Office patent fileor records, but otherwise reserves all copyright rights whatsoever.

TECHNICAL FIELD

The present invention relates to methods and corresponding apparatus forregulated and efficient DC-to-AC conversion with high power quality, andto methods and corresponding apparatus for regulation and control ofsaid DC-to-AC conversion. The invention further relates to methods andcorresponding apparatus for regulation and control of AC-to-DC and/orDC-to-DC conversion.

BACKGROUND

A power inverter, or an inverter, or a DC-to-AC converter, is anelectronic device or circuitry that changes direct current (DC) toalternating current (AC) (e.g. single- and/or 3-phase).

A power inverter would typically be a switching inverter that uses aswitching device (solid-state or mechanical) to change DC to AC. Thereare may be many different power circuit topologies and controlstrategies used in inverter designs. Different design approaches addressvarious issues that may be more or less important depending on the waythat the inverter is intended to be used. For example, an inverter mayuse an H bridge that is built with four switches (solid-state ormechanical), that enables a voltage to be applied across a load ineither direction.

Given a particular power circuit topology, an appropriate controlstrategy may need to be chosen in order to meet the desired inverterspecifications, e.g. in terms of input and output voltages, AC andswitching frequencies, output power and power density, power quality,efficiency, cost, and so on.

For example, one of the most obvious approaches to increase powerdensity would be to increase the frequency that the inverter operates at(“switching frequency”). This may be done by employing wide-bandgap(WBG) semiconductors that use materials such as gallium nitride (GaN) orsilicon carbide (SiC) and can function at higher power loads andfrequencies, allowing for smaller, more energy-efficient devices.

A typical way to control a switching inverter is mathematically definingvoltage and/or current relations at different switching states toproduce the “desired” output, obtaining the appropriate digitallysampled voltage and/or current values, then using numerical signalprocessing tools to implement an appropriate algorithm to control theswitches [1]. However, such a straightforward approach often calls forperformance compromises based on the ability to accurately define thevoltage and current relations for various topological stages and loadconditions (e.g. nonlinear loads), and to account for nonidealities andtime variances of the components (since the values of, e.g.,resistances, capacitances, inductances, switches' behavior etc. maychange in time due to the temperature changes, mechanicalstress/vibrations, aging, etc.). In addition, a control processor forthe inverter must meet a number of real-time processing challenges,especially at high switching frequencies, in order to effectivelyexecute the algorithms required for efficient DC/AC conversion andcircuit protection. Various design and implementation compromises areoften made in order to overcome these challenges, and those cannegatively impact the complexity, reliability, cost, and performance ofthe inverter.

Thus there is a need in a simple analog (i.e. continuous and real-time)controller that would allow us to bypass the detailed analysis ofvarious topological stages during a switching cycle altogether, thusavoiding the pitfalls and limitations of straightforward digitaltechniques.

Further, there is a need in such a simple controller that (i) does notrequire any current sensors, or additional start-up and managementmeans, (ii) provides robust, high quality (e.g. low voltage and currentharmonic distortions), and well regulated AC outputs for a wide range ofpower factor loads, including highly nonlinear loads, and also (iii)offers multiple ways to optimize the cost-size-weight-performancetradespace.

SUMMARY

The present invention overcomes the limitations of the prior art byintroducing an Inductor Current Mapping, or ICM controller. The ICMcontroller offers various overall advantages over respective digitalcontrollers, and may provide multiple ways to optimize thecost-size-weight-performance tradespace.

In the detailed description that follows, we first introduce anidealized concept of an analog ICM controller for an H-bridge powerinverter. We show how the “actual” voltage-current relations in thefilter inductors may be directly “mapped,” by the constraints imposedtwo Schmitt triggers, to the voltage relations among the inputs and theoutput of the controller's analog integrator, providing the desiredinverter output that is effectively proportional to the referencevoltage. We then discuss the basic operation and properties of thisinverter and its associated ICM controller, using particularimplementations for illustration. Further, we describe a simplecontroller modification that may improve the transient responses byutilizing a feedback signal proportional to the load current. Next, wediscuss extensions of the ICM concept to other hard- or soft-switchingpower inverters (e.g. for 3-phase inverters), and for AC/DC and DC/DCconverter topologies, and the use of ICM controllers in DC/DC convertersfor voltage, current, and power regulation.

Further scope and the applicability of the invention will be clarifiedthrough the detailed description given hereinafter. It should beunderstood, however, that the specific examples, while indicatingpreferred embodiments of the invention, are presented for illustrationonly. Various changes and modifications within the spirit and scope ofthe invention should become apparent to those skilled in the art fromthis detailed description. Furthermore, all the mathematicalexpressions, diagrams, and the examples of hardware implementations areused only as a descriptive language to convey the inventive ideasclearly, and are not limitative of the claimed invention.

BRIEF DESCRIPTION OF FIGURES

FIG. 1. Basic diagram of an asynchronous buck inverter of the presentinvention and its associated controller.

FIG. 2. Alternative grounding configuration of the inverter and itsassociated controller shown in FIG. 1.

FIG. 3. Illustrative steady-state voltage and current waveforms for theinverter and its associated controller shown in FIGS. 1 and 2. Low FCSfrequency (6 kHz) is used for better waveform visibility.

FIG. 4. Illustrative transient voltage and current waveforms for theinverter and its associated controller shown in FIGS. 1 and 2. Low FCSfrequency (6 kHz) is used for better waveform visibility.

FIG. 5. Illustrative schematic of a controller circuit implementation.

FIG. 6. Illustrative schematic of a particular implementation of theinverter and its associated controller shown in FIG. 1.

FIG. 7. Simulated MOSFET and total power losses, efficiency, and totalharmonic distortions as functions of the output power for the particularinverter implementation shown in FIG. 6 (48 kHz FCS, resistive low).

FIG. 8. Illustrative steady-state voltage and current waveforms for alagging PF=0.5 load (66.2 mH inductor in series with 14.4Ω resistor),for the inverter and its associated controller shown in FIG. 6 (48 kHzFCS).

FIG. 9. Illustrative transient voltage and current waveforms for alagging PF load (50 mH inductor in series with 10.8Ω or 84.4Ωresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 10. Illustrative steady-state voltage and current waveforms for aleading PF=0.5 load (106 μF capacitor in series with 14.4Ω resistor),for the inverter and its associated controller shown in FIG. 6 (48 kHzFCS).

FIG. 11. Illustrative transient voltage and current waveforms for aleading PF load (70.7 μF capacitor in series with 21.6Ω or 1 MΩresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 12. Illustrative schematic of a particular implementation of afree-running version of the inverter and its associated controller shownin FIG. 1.

FIG. 13. Power spectra of the common and differential mode outputvoltages for the particular FCS-based (FIG. 6) and free-running (FIG.12) implementations. The vertical dashed lines are at 150 kHz.

FIG. 14. An H-bridge inverter with a free-running ICM controller.

FIG. 15. Example of full-range transient waveforms for ohmic load.

FIG. 16. Transient waveforms for nonlinear (full-wave diode rectifier)load (2 kW).

FIG. 17. Transient waveforms for changes in V_(ref) (“instantaneous”synchronization with reference).

FIG. 18. Illustrative steady state waveforms at full (2 kW) resistiveload.

FIG. 19. Illustrative steady state waveforms at 10% (200 W) resistiveload.

FIG. 20. Full-load (2 kW) waveforms on 2.8 ms to 3 ms interval.

FIG. 21. 10%-load (200 W) waveforms on 2.8 ms to 3 ms interval.

FIG. 22. PSD of inductor current at full and 10% loads.

FIG. 23. Efficiency and THD as functions of output power.

FIG. 24. Illustrative startup voltages and currents.

FIG. 25. Inverter and ICM controller with load current feedback.

FIG. 26. Transient responses for leading PF=0.5 load without (left) andwith (right) current feedback.

FIG. 27. Buck-boost DC/DC converter with ICM controller.

FIG. 28. Example of transient waveforms for the converter shown in FIG.27 configured for voltage, current, and power regulation.

FIG. 29. Startup voltages and currents for the buck-boost DC/DCconverter with ICM controller.

FIG. 30. Illustrative example of an ICM-controlled 3-phase inverter.

FIG. 31. Example of full-range transient waveforms for theICM-controlled 3-phase inverter shown in FIG. 30.

FIG. 32. Startup voltages and currents when the 3 kW ICM-controlled3-phase inverter shown in FIG. 30 is connected to a low (p.f.=0.1)lagging power factor load in Δ configuration, with the apparent power ofabout 3 kW.

FIG. 33. Example of a single-phase H-bridge ICM-based AC/DC converterwith high power factor and low harmonic distortions.

FIG. 34. Illustration of the behavior of a particular implementation ofa 2 kW ICM-controlled single-phase AC/DC converter shown in FIG. 33.

FIG. 35. Illustration of variations in ICM controller topologies.

FIG. 36. Example of a 3-phase ICM-based AC/DC converter with high powerfactor and low harmonic distortions.

FIG. 37. Illustration of the behavior of a particular implementation ofa 6 kW ICM-controlled 3-phase AC/DC converter shown in FIG. 36.

FIG. 38. PSDs of line currents and −V_(CM)−V_(N) for a particularimplementation of a 6 kW ICM-controlled 3-phase AC/DC converter shown inFIG. 36.

FIG. 39. Example of ICM-based control of a 3-phase AC/DC converter thatis effectively equivalent to that shown in FIG. 36.

FIG. 40. Illustrative example of using the 3-phase AC/DC convertersshown in FIG. 36 and FIG. 39 for 3-phase DC/AC conversion.

FIG. 41. Illustration of transient output power, voltages and currents,and the inductor currents, for a particular implementation of a 6 kWICM-controlled 3-phase inverter shown in FIG. 40, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

FIG. 42. Analog and digital ICM implementations.

FIG. 43. Illustration of effective equivalence of analog and digital ICMimplementations.

FIG. 44. Illustration of effective equivalence of analog and digital ICMimplementations for oversampled 8-bit digital representations of analogvoltages (without lowpass filtering in the digital implementation).

FIG. 45. Principal schematic of a 3-phase 6-switch rectifier thatincorporates the power stage, LC EMI filtering network (componentswithin the dashed-line boundary), and low-power analog circuitry thatprovides both the control of the power stage and non-dissipativeresonance damping of the EMI filters.

FIG. 46. Transient responses under mains voltage imbalance for aparticular implementation of an ICM-based 3-phase rectifier shown inFIG. 45, for 115 VAC to 400 VDC conversion with ƒ_(AC)=500 Hz.

FIG. 47. Efficiency/losses breakdown, PF, and THD for a particularimplementation of an ICM-based 3-phase rectifier shown in FIG. 45, for115 VAC to 400 VDC conversion with ƒ_(AC)=500 Hz.

FIG. 48. Steady-state line currents and CM/DM voltages at 10 kW outputfor a particular implementation of an ICM-based 3-phase rectifier shownin FIG. 45, for 115 VAC to 400 VDC conversion with ƒ_(AC)=500 Hz.

FIG. 49. Steady-state switching voltages (at 10 kW/output) for aparticular implementation of an ICM-based 3-phase rectifier shown inFIG. 45, for 115 VAC to 400 VDC conversion with ƒ_(AC)=500 Hz.

FIG. 50. Three-level ICM control of an H-bridge inverter.

FIG. 51. Illustration of performance of a 3-level ICM-controlledH-bridge inverter of FIG. 50 in comparison with a respective 2-levelinverter with the same power stage components.

FIG. 52. Grid setting/following 3-level ICM-controlled H-bridgeconverter used in the simulations of Section 11.

FIG. 53. Paralleled PV/battery ICM-based H-bridge converters poweringnonlinear load.

FIG. 54. DC voltages V_(DC) and V′_(DC), the DC powers(P_(DC)=I_(DC)V_(DC) and P′_(DC)=I′_(DC)V′_(DC)), the output (load)voltage V_(AC) and current I_(load), and the output voltage of therectifier V_(rec) for the setup of FIG. 53.

ABBREVIATIONS

AC: alternating (current or voltage); A/D: Analog-to-Digital; ADC;Analog-to-Digital Converter (or Conversion);

BCM: Boundary Conduction Mode; BOM: Bill Of Materials;

CCM: Continuous Conduction Mode; CM: Common Mode; COTS: CommercialOff-The-Shelf;

DC: direct (current or voltage), or constant polarity (current orvoltage); DCM: Discontinuous Conduction Mode; DCR: DC Resistance of aninductor; DM: Differential Mode; DSP: Digital SignalProcessing/Processor;

EMC: electromagnetic compatibility; e.m.f.: electromotive force; EMI:electromagnetic interference; ESR: Equivalent Series Resistance;

FCS: Frequency Control Signal; FFT: Fast Fourier Transform; GaN: Galliumnitride;

ICM: Inductor Current Mapping; IGBT: Insulated-Gate Bipolar Transistor;

LC: inductor-capacitor;

MATLAB: MATrix LABoratory (numerical computing environment andfourth-generation programming language developed by MathWorks); MEA:More Electric Aircraft; MOS: Metal-Oxide-Semiconductor; MOSFET: MetalOxide Semiconductor Field-Effect Transistor; MTBF: Mean Time BetweenFailures; NDL: Nonlinear Differential Limiter;

PF: Power Factor; PFC: Power Factor Correction; PFM: Pulse-FrequencyModulation; PoL: Point-of-Load; PSD: Power Spectral Density; PSM: PowerSave Mode; PV: Photovoltaic/Photovoltaics; PWM: Pulse-WidthModulation/Modulator;

RFI: Radio Frequency Interference; RMS: Root Mean Square;

SCS: Switch Control Signal; SiC: Silicon carbide; SMPS: Switched-ModePower Supply; SMVF: Switched-Mode Voltage Follower; SMVM: Switched-ModeVoltage Mirror; SNR: Signal to Noise Ratio; SCC: Switch Control Circuit;

THD: Total Harmonic Distortion;

UAV: Unmanned Aerial Vehicle; ULISR: Ultra Linear Isolated SwitchingRectifier; ULSR(U): Ultra Linear Switching Rectifier (Unit);

VN: Virtual Neutral; VRM: Voltage Regulator Module; WBG: wide-bandgap;

ZVS: Zero Voltage Switching; ZVT: Zero Voltage Transition;

DETAILED DESCRIPTION 1 Illustrative Description of an Asynchronous BuckInverter of the Present Invention and of its Principles of Operation

Let us first consider the simplified circuit diagram shown in FIG. 1.

This power inverter would be capable of converting the DC source voltageV_(in) into the AC output voltage V_(out) that is indicative of the ACreference voltage V_(ref).

In FIG. 1, the DC source voltage V_(in) is shown to be provided by abattery, and the resistor connected in series with the battery indicatesthe battery's internal resistance.

Capacitance of the capacitor connected in parallel to the battery wouldneed to be sufficiently large (for example, of order 10 μF) to provide arelatively low impedance path for high-frequency current components. Asignificantly larger capacitance may be used (e.g., of order 1 mF,depending on the battery's internal resistance) to reduce the lowfrequency (e.g., twice the AC frequency) input current and voltageripples.

In FIG. 1, the DC source voltage V_(in) is shown to be applied to theinput of the H bridge comprising two pairs of switches (labeled “1” and“2”), and the output voltage of the H bridge is the switching voltageV*. For example, when the switches of the 2nd pair are “on” and theswitches of the 1st pair are “off”, V* would be effectively equal toV_(in), and when the switches of the 1st pair are “on” and the switchesof the 2nd pair are “off”, V* would be effectively equal to −V_(in).

The diodes explicitly shown in FIG. 1 as connected across the switchesin the bridge would enable a non-zero current through the inductors whenall switches in the bridge are “off”. All switches in the bridge being“off” may be viewed as asynchronous state of the inverter. During theasynchronous state, and depending on the magnitude and the direction ofthe current through the inductors, the switching voltage V* may havevalues between −V_(in) and V_(in).

One skilled in the art will recognize that, for example, if the switchesare implemented using power MOSFETs, the diodes explicitly shown in FIG.1 may be the MOSFET body diodes.

The switching voltage V* is further filtered with an LC filteringnetwork to produce the output voltage V_(out). In FIG. 1, this networkperforms both differential mode (DM) filtering to produce the outputdifferential voltage V_(out), and common mode (CM) filtering to reduceelectromagnetic interference (EMI). The DM filtering bandwidth of the LCnetwork should be sufficiently narrow to suppress the switchingfrequency and its harmonics, while remaining sufficiently larger thanthe AC frequency.

The DM inductance L in FIG. 1 may be provided by physical inductors, byleakage inductance of the CM choke, or by combination thereof.

The switches of the 1st and 2nd pairs in the bridge are turned “on” or“off” by the respective switch control signals (SCSs), labeled as Q₁ andQ₂, respectively, in FIG. 1. In the figure, it is implied that theswitches are turned “on” by a high value of the respective SCS, and areturned “off” by the low value of the SCS.

In FIG. 1, the input to the integrator (with the integration timeconstant T) is a sum of the AC reference voltage V_(ref) and a voltageproportional to the switching voltage, μV*, and the output of theintegrator contributes to the input of both inverting and non-invertingcomparators. The comparators may also be characterized by sufficientlylarge hysteresis, e.g., be configured as Schmitt triggers.

When the comparators are configured as Schmitt triggers, the frequencycontrol signal (FCS) V_(FCS) may be optional, as would be discussedfurther in the disclosure. Such a configuration of the inverter (withoutan FCS) would be a free-running configuration.

A (constant) positive threshold offset, or FCS offset, signal ΔV_(FCS)is added to the input of the non-inverting comparator in FIG. 1. Thisoffset signal enables the SCSs Q₁ and Q₂ to simultaneously have lowvalues, thus keeping all switches in the bridge “off”, and thus enablingan asynchronous state of the inverter.

A periodic FCS V_(FCS) may be added to the inputs of both inverting andnon-inverting comparators to enable switching at typically constant(rather than variable) frequency, effectively equal to the FCSfrequency.

A signal proportional to the output AC voltage,

${\mu\frac{\tau}{T}V_{out}},$is added to the inputs of both inverting and non-inverting comparatorsfor damping transient responses of the inverter caused by changes in theload (load current). The mechanism of such damping, and the choice ofthe three parameter T, would be discussed further in the disclosure. Oneskilled in the art will recognize that, equivalently, a signalproportional to the time derivative of the output AC voltage, μτ{dotover (V)}_(out), may be added to the input of the integrator.

It may be important to point out that the output AC voltage V_(out) ofthe inverter of the present invention would be effectively independentof the DC source voltage V_(in), as long as (neglecting the voltagedrops across the switches and the inductors) |V_(in)| is larger than|V_(out)|.

The grounding configuration of the inverter shown in FIG. 1 would beappropriate for the 240 V split phase configuration, similar to whatwould be found in North American households.

FIG. 2 shows the modification of the inverter appropriate for the 240V-to-ground configuration, similar to what would be found in Europeanand other households around the world.

One skilled in the art will recognize that the configuration shown inFIG. 2 would allow combining outputs of multiple such inverters into amulti-phase output.

FIG. 3 shows illustrative steady-state voltage and current waveforms forthe inverter and its associated controller shown in FIGS. 1 and 2. LowFCS frequency (6 kHz) is used for better waveform visibility.

FIG. 4 shows illustrative transient voltage and current waveforms forthe inverter and its associated controller shown in FIGS. 1 and 2. LowFCS frequency (6 kHz) is used for better waveform visibility.

In both FIG. 3 and FIG. 4, low FCS frequency (6 kHz) was used for betterwaveform visibility, and the switches were implemented using SiC powerMOSFETs.

FIG. 5 provides an illustrative schematic of a controller circuitimplementation.

One may see that this controller comprises an (inverting) integratorcharacterized by an integration time constant T, where the integratorinput comprises a sum of (1) the signal proportional to the switchingvoltage, μV*, (2) the reference AC voltage V_(ref), and (3) the signalproportional to the time derivative of the output AC voltage, μτ{dotover (V)}_(out).

The controller further comprises two comparators outputting the SCSs Q₁and Q₂.

A sum of the integrator output and the FCS V_(FCS) (which is a periodictriangle wave in this example) is supplied to the positive terminal ofthe comparator providing the output Q₁, and to the negative terminal ofthe comparator providing the output Q₂.

The reference thresholds for the comparators are provided by a resistivevoltage divider as shown in the figure, and the threshold value suppliedto the negative terminal of the comparator providing the output Q₂ isΔV_(FCS) larger than the threshold value supplied to the positiveterminal of the comparator providing the output Q₁.

To further illustrate the essential features of the asynchronous buckinverter of the present invention, and of its associated controller, letus consider a particular implementation example shown in FIG. 6.

Note that in this example the capacitance of the capacitor connected inparallel to the battery is only 10 μF. It would provide a relatively lowimpedance path for high-frequency current components. However, asignificantly larger capacitance (e.g., of order 1 mF, depending on thebattery's internal resistance) should be used to reduce the lowfrequency (e.g. twice the AC frequency) input current and voltageripples.

FIG. 7 shows simulated MOSFET and total power losses, efficiency, andtotal harmonic distortions as functions of the output power for theparticular inverter implementation shown in FIG. 6 (48 kHz FCS,resistive load).

FIG. 8 provides illustrative steady-state voltage and current waveformsfor a lagging PF=0.5 load (66.2 mH inductor in series with 14.4Ωresistor), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 9 provides illustrative transient voltage and current waveforms fora lagging PF load. (50 mH inductor in series with 10.8Ω or 84.4Ωresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 10 provides illustrative steady-state voltage and current waveformsfor a leading PF=0.5 load (106 μF capacitor in series with 14.4Ωresistor), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

FIG. 11 provides illustrative transient voltage and current waveformsfor a leading PF load (70.7 μF capacitor in series with 21.6Ω or 1 MΩresistors), for the inverter and its associated controller shown in FIG.6 (48 kHz FCS).

2 Free-Running (Variable Frequency) Configuration of an Inverter of thePresent Invention

FIG. 12 shows an illustrative schematic of a particular implementationof a free-running version of the inverter and its associated controllershown in FIG. 1.

In a free-running configuration, the switching frequency varies with theoutput voltage, and its average value would depend on the input andoutput voltages and the load, and would be generally inverselyproportional to the value of the hysteresis gap of the Schmitt triggersand the time constant of the integrator.

With the components and the component values shown in FIG. 12, theinverter typically (e.g., in a steady state) operates in a discontinuousconduction mode (DCM) for the output powers ≲2.2 kW, and the modulationtype may be viewed as effectively a pulse-frequency modulation.

To illustrate the differences in switching behavior, FIG. 13 shows thepower spectra of the common (CM) and differential mode (DM) outputvoltages for the particular FCS-based (FIG. 6) and free-running (FIG.12) implementations. The vertical dashed lines are at 150 kHz.

3 Detailed Description of Basic Operation of an H-Bridge Inverter with aFree-Running ICM Controller

FIG. 14 shows a simplified schematic of a H-bridge inverter with afree-running ICM controller. As may be seen in the figure, the MOSFETswitches in the bridge are turned on or off by high or low values,respectively, of the switch control signals (SCS) Q₁ and Q₂ provided bythe controller, and the bridge outputs the switching voltage V*. Theswitching voltage is then filtered with a passive LC filtering networkto produce the output voltage V_(out). The ICM controller effectivelyconsists of (i) an integrator (with the time constant T) integrating asum of three inputs, and (ii) two Schmitt triggers with the samehysteresis gap Δh, inverting (outputting Q₁) and non-inverting(outputting Q₂). A resistive divider ensures that the reference voltageof the non-inverting Schmitt trigger is slightly higher than that of theinverting one.

For the performance examples in this section that follow, the componentsand their nominal values are as follows:

The battery electromotive force (e.m.f.) is ε=450 V; the battery'sinternal resistance is 10Ω; the capacitance of the capacitor connectedin parallel to the battery is 1,200 μF; the switches are the CreeC2M0025120D SiC MOSFETs; the diodes in parallel to the switches are theRohm SCS220KGC SiC Schottky diodes; the OpAmps are LT1211; thecomparators are LT1715; L=195 μH; C=4 μF; μ=1/200; R=10 kQ; T=47 μs(T/R=4.7 nF); T=22 μs (T/R=2.2 nF); V_(s)=5 V; R′=10 kΩ; δ R′=510Ω;r=100 kΩ, and δ r=10 kΩ.

Let us initially make a few sensible idealizations, including nearlyideal behavior of the controller circuit, insignificant voltage dropsacross the components of the bridge, negligible ohmic voltage dropsacross the reactive components, and approximately constant L and C. Wewould also assume a practical choice of T and Δh that would ensuresufficiently high switching frequencies for the switching ripples in theoutput voltage to be ignored, as they would be adequately filtered bythe LC circuit. This would imply that we may consider an instantaneousvalue of V_(out) within a switching cycle to be effectively equal to theaverage value of V_(out) over this cycle. With such idealizations, andprovided that |V_(ref)|<μ|V_(in)| at all times, the output voltageV_(out) may be expressed, in reference to FIG. 14, by the followingequation:

$\begin{matrix}{{{\overset{\_}{V}}_{out} = {\left( {{- \frac{{\overset{\_}{V}}_{ref}}{\mu}} - {2L{\overset{\overset{.}{\_}}{I}}_{load}}} \right) - {\tau{\overset{\overset{.}{\_}}{V}}_{out}} - {2{LC}{\overset{\overset{¨}{\_}}{V}}_{out}}}},} & (1)\end{matrix}$where I_(load) is the load current, the overdots denote timederivatives, μ is the nominal proportionality constant between thereference and the output voltages, and the overlines denote averagingover a time interval between a pair of rising or falling edges of eitherQ₁ or Q₂. Thus, according to equation (1), the output voltage of theinverter shown in FIG. 14 would be equal to the voltage −V _(ref)/μ−2Lİ_(load) filtered with a 2nd order lowpass filter with the undampednatural frequency ω_(n)=1√{square root over (2LC)} and the qualityfactor Q=√{square root over (2LC)}/T. The reference voltage V_(ref) inequation (1) may be an internal reference (e.g. for operating in anislanded mode), or an external reference (e.g. it may be proportional tothe mains voltage for synchronization with the grid).

3.1 Derivation of Equation (1)

Let us show how equation (1) may be derived by mapping the voltage andcurrent relations in the output LC filter to the voltage relations amongthe inputs and the output of the integrator in the ICM controller.

Indeed, for a continuous function ƒ(t), the time derivative of itsaverage over a time interval ΔT may be expressed as

$\begin{matrix}{{{\overset{\overset{.}{\_}}{f}(t)} = {{\frac{d}{dt}\left\lbrack {\frac{1}{\Delta\; T}{\int_{t - {\Delta\; T}}^{t}{{ds}\mspace{14mu}{f(s)}}}} \right\rbrack} = {\frac{1}{\Delta\; T}\left\lbrack {{f(t)} - {f\left( {t - {\Delta\; T}} \right)}} \right\rbrack}}},} & (2)\end{matrix}$and it will be zero if ƒ(t)−ƒ(t−ΔT)=0.

Note that rising and falling edges of an output of a Schmitt triggerhappen when its input crosses (effectively constant) respectivethresholds. Thus relating the inputs and the output of the integrator inthe ICM controller, differentiating both sides, then averaging between apair of rising or falling edges of either Q₁ or Q₂, would lead to

$\begin{matrix}{{\overset{\_}{V}}^{*} = {{- \frac{{\overset{\_}{V}}_{ref}}{\mu}} - {\tau{{\overset{\overset{.}{\_}}{V}}_{out}.}}}} & (3)\end{matrix}$On the other hand, from the voltage and current relations in the outputLC filter,V*=V _(out)+2Lİ _(load)+2LC{dot over (V)} _(out),  (4)and equating the right-hand sides of (3) and (4) would lead to equation(1).

3.2 Transient Responses

For convenience, we may define the “no-load ideal output voltage”V_(ideal) as

$\begin{matrix}{V_{ideal} = {{- \frac{V_{ref}}{\mu}} - {\tau\;{\overset{.}{V}}_{ideal}} - {2{LC}{{\overset{¨}{V}}_{ideal}.}}}} & (5)\end{matrix}$Then equation (1) may be rewritten as

$\begin{matrix}{{\overset{\_}{v} = {{{- \frac{2\mu\; L}{V_{0}}}{\overset{\overset{.}{\_}}{I}}_{load}} - {\tau\overset{.}{\overset{\_}{v}}} - {2{LC}\overset{\overset{¨}{\_}}{v}}}},} & (6)\end{matrix}$where v is a nondimensionalized error voltage that may be defined as thedifference between the actual and the ideal outputs in relation to themagnitude of the ideal output, for example, as

$\begin{matrix}{{v = \frac{V_{out} - V_{ideal}}{\max{V_{ideal}}}},} & (7)\end{matrix}$where max |V_(ideal)| is the amplitude of the ideal output. For asinusoidal reference V_(ref)=V₀ sin (2πƒ_(AC)t), and provided that Q≲1and Tf_(AC)<<<1, the no-load ideal output would be different from−V_(ref)/μ by only a relatively small time delay and a negligible changein the amplitude. Then v may be expressed as v=μ(V_(out)−V_(ideal))/V₀.

Note that the symbol ≲ may be read as “smaller than or similar to” andthe symbol <<< may be understood as “two orders or more smaller than”.

Thus, according to equation (6), the transients in the output voltage(in addition to the “normal” switching ripples at constant load) wouldbe proportional to the time derivative of the load current filtered witha 2nd order lowpass filter with the undamped natural frequencyω_(n)=1/√{square root over (2LC)} and the quality factor Q=√{square rootover (2LC)}/T. Note that the magnitude of these transients would also beproportional to the output filter inductance L.

For example, for a step change at time t=t₀ in the conductance G of anohmic load, from G=G₁ to G=G₂, equation (6) would become

$\begin{matrix}{{\overset{\_}{v} = {{{- \frac{2\mu\;{{LV}_{out}\left( t_{0} \right)}}{V_{0}}}\left( {G_{2} - G_{1}} \right)\overset{\_}{\delta\left( {t - t_{0}} \right)}} - {\left\{ {\tau + {2{L\left\lbrack {{G_{1}\overset{\_}{\theta\left( {t_{0} - t} \right)}} + {G_{2}\overset{\_}{\theta\left( {t - t_{0}} \right)}}} \right\rbrack}}} \right\}\overset{.}{\overset{\_}{v}}} - {2{LC}\overset{\overset{¨}{\_}}{v}}}},} & (8)\end{matrix}$where θ(x) is the Heaviside unit step function [2] and δ (x) is theDirac δ-function [3]. In equation (8), the first term is the impulsedisturbance due to the step change in the load current, and V_(out)(t₀)is the output voltage at t=t₀. Note that δ (t−t₀) would be zero if t₀lies outside of the averaging interval ΔT, and would be equal to 1/ΔTotherwise.

Note that formally δ (t−t₀)=1/(2ΔT) when t₀ is exactly at the beginningor at the end of the averaging interval.

FIG. 15 provides an example of illustrative transient voltage andcurrent waveforms for a particular implementation of the inverter andits associated ICM controller shown in FIG. 14, in response tofull-range step changes in a resistive load. Note that the switchinginterval, as well as the inductor current and its operation mode (e.g.continuous (CCM) or discontinuous (DCM) change according to the outputvoltage values and the load conditions, and would also change accordingto the power factor of the load.

It is also instructive to illustrate the robustness and stability ofthis inverter for other highly nonlinear loads. (A nonlinear electricalload is a load where the wave shape of the steady-state current does notfollow the wave shape of the applied voltage (i.e. impedance changeswith the applied voltage and Ohm's law is not applicable)). FIG. 16provides an example of voltage and current waveforms when the inverterwith its associated ICM controller shown in FIG. 14 is connected to afull-wave diode rectifier powering a 2 kW load.

FIG. 1, provides an example of transient voltage and current waveforms,for the same inverter, in response to connecting and disconnecting thereference voltage. This shows the “instantaneous” synchronization withreference, e.g., illustrating how the presented inverter may quicklydisconnect from and/or reconnect to the grid when used as a grid-tieinverter.

3.3 Switching Behavior and Efficiency Optimization

From the above mathematical description one may deduce that, for giveninductor and capacitor values, and for given controller parameters(e.g., T and Δh), the total switching interval (i.e., the time intervalbetween an adjacent pair of rising or falling edges of either Q₁ or Q₂),the duty cycle, and the “on” and “off” times, would all vary dependingon the values and time variations of V_(in), V_(ref), V_(out), and theload current. Thus the switching behavior of the ICM controller may notbe characterized in such simple terms as pulse-width or pulse-frequencymodulation (PWM or PFM). This is illustrated in FIGS. 18 through 21,which show representative steady state waveforms at full (2 kW), and 10%(200 W) resistive loads.

In a steady state (i.e. for a constant load), the average value of theswitching interval would be generally proportional to the product of theintegrator time constant T and the hysteresis gap Δh of the Schmitttriggers (i.e. the values of r and δ r). The particular value of theswitching interval would also depend on the absolute value of thereference voltage |V_(ref)| (as ∝ |V_(ref)|⁻¹), on the ratio|V_(ref)|/|V_(in)|, and on the load current [4, 5]. As a result, even ina steady state, for a sinusoidal AC reference the switching frequencywould span a continuous range of values, as illustrated in FIG. 22,which shows the power spectral density (PSI)) of the inductor current atfull (2 kW) and 10% (200 W) resistive loads.

For given inverter components and their values, the power losses invarious components would be different nonlinear functions of the load,and would also exhibit different nonlinear dependences on the integratortime constant T and the hysteresis gap Δh. Thus, given a particularchoice of the MOSFET switches and their drivers, the magnetics, andother passive inverter components, by adjusting T and/or Δh one mayachieve the best overall compromise among various component power losses(e.g., between the bridge and the inductor losses), while remainingwithin other constraints on the inverter specifications.

FIG. 23 provides an example of simulated efficiency and total harmonicdistortion (THD) values as functions of the output power for aparticular inverter implementation using commercial off-the-shelf (COTS)components (including SiC MOSFETs and diodes), with the specificationsaccording to the technical requirements for the Little Box Challenge [6]outlined in [7]. In the efficiency simulations, high-fidelity modelswere used for the MOSFETs and diodes, and the inductor core and windinglosses were taken into account. The dashed line in the upper panel ofFIG. 23 plots the simulated efficiency with more conservative (doubled)estimated total losses, including the MOSFET and the inductor losses.

3.4 Startup Behavior

FIG. 24 illustrates the startup voltages (upper panel) and currents(lower panel) for a full (2 kW) resistive load connected to the outputof the inverter. As one may see, as long as the controller is poweredup, the battery may be connected to the input of the inverter (at 12.5ms in the figure), and the output voltage would quickly converge to thedesired output without excessive inrush currents and/or voltagetransients. The only significant inrush current may be the initialcurrent through the battery, charging the inverter's input capacitorduring the time interval comparable with the product of the inputcapacitor and the battery's internal resistance.

3.5 Improving Transient Response by Introducing Feedback of the LoadCurrent

One may infer from equation (1) that the term −2Lİ _(load) may becancelled by adding −2 μLİ_(load) to the input of the integrator.However, the switching ripples in the load current would normally makesuch an approach impractical. Instead, one should add a voltage2μLI_(load)/T directly to the inputs of the Schmitt triggers, asillustrated in FIG. 25.

Additionally, because of the propagation delays and other circuitnonidealities, fast step current transients may not be cancelledexactly. Instead, the current feedback would try to “counteract” animpulse disturbance in the output voltage due to a step change in theload current by a closely following pulse of opposite polarity, mainlyreducing the frequency content of the transients that lies below theswitching frequencies. This is illustrated in FIG. 6, which compares thetransient responses for an ICM controller without (left) and with(right) current feedback, when a leading PF=0.5 load is connected to anddisconnected from the output of the inverter with the frequency 1 kHzand 50% duty cycle. As indicated by the horizontal lines in the lowerpanels of the example of FIG. 26, the current feedback reduces the PSDof the transients at the load switching frequency (1 kHz) approximately12 dB.

4 Buck-Boost DC/DC Converter with ICM Controller

While above the ICM controller is disclosed in connection with a hardswitching H-bridge power inverter, the ICM concept may be extended, withproper modifications, to other hard- or soft-switching power inverterand DC/DC converter topologies.

As an illustration, FIG. 27 provides an example of a buck-boost DC/DCconverter with an ICM controller. When the feedback voltage V_(fb) isproportional to the output voltage, V_(fb)=−V_(out)/β, this converterwould provide an output voltage regulation with the nominal steady-stateoutput voltage βV_(ref). When the feedback voltage V_(fb) isproportional to the load current, V_(fb)=−

I*/β, this converter would provide an output current regulation with thenominal steady-state output current βV_(ref)/R. Note that in thisexample the load explicitly contains a (parallel) capacitance that maybe comparable with, or larger than, the converter capacitance C, andthus the feedback voltage may contain very strong high-frequencycomponents. Further, when the feedback voltage V_(fb) is proportional tothe output power, V_(fb)=−V_(out)I*/I₀/β, this converter would providean output power regulation with the nominal steady-state output powerβV_(ref)I₀.

FIG. 28 provides an example of transient waveforms for a particularimplementation of the converter shown in FIG. 27 configured for voltage,current, and power regulation.

For an isolated version, the converter inductor may be replaced by aflyback transformer, as indicated in the upper right corner of FIG. 27.

4.1 Startup Sequence for the Buck-Boost DC/DC Converter with ICMController

For a proper startup of the converter shown in FIG. 27, the initialvalue of the reference voltage V_(ref) should be zero. After both thecontroller circuit and the power stage are powered up, the referencevoltage should be ramped up from zero to the desired value over sometime interval. The duration of this time interval would depend on theconverter specifications and the component values, and would typicallybe in the 1 ms to 100 ms range.

For a particular implementation of the converter, FIG. 29 illustratesthe startup voltages and currents for a full resistive load connected tothe output of the converter (upper panel), and for no load at the output(lower panel). In this illustration, the controller circuit is poweredup first, with the reference voltage set to zero. At 5 ms, the batteryis connected to the converter input. At 10 ms, the reference voltagestarts ramping up from zero, reaching its desired value at 20 ms. As onemay see, with such a startup sequence there would be no excessively highinrush currents through the converter inductor.

5 ICM Control of 3-Phase Inverters

FIG. 30 provides an example of an ICM-controlled 3-phase inverter. Here,the output line-to-line voltages V_(ab), V_(bc), and V_(ca) would beproportional to the respective reference voltages V_(ab), V_(bc), andV_(ca); where V_(ab)+V_(bc)+V_(ca)=0. Note that, in general, thereference voltages do not need to be sinusoidal signals.

As one should be able to see in FIG. 30, the switches in the bridge arecontrolled by three instances of an ICM controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

The switching voltages V_(ab)*, V_(bc)*, and V_(ca)* are the differencesbetween the voltages at nodes a, b, and c: V_(ab)*=V_(a)*−V_(b)*,V_(bc)*=V_(b)*−V_(c)*, and V_(ca)*=V_(c)*−V_(a)*.

This inverter is characterized by the advantages shared with theH-bridge inverter presented above: robust, high quality, andwell-regulated AC output for a wide range of power factor loads,voltage-based control without the need for separate start-up management,the ability to power highly nonlinear loads, effectively instantaneoussynchronization with the reference (allowing to quickly disconnect fromand/or reconnect to the grid when used as a grid-tie inverter), andmultiple ways to optimize efficiency and thecost-size-weight-performance tradespace.

For example, FIG. 31 illustrates transient output voltages and currents,and the inductor currents, for a particular implementation of a 3 kWICM-controlled 3-phase inverter shown in FIG. 30, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

Note that for 3-phase loads that are not significantly unbalanced, thevalue of the input capacitor may be significantly reduced, in comparisonwith the single-phase H-bridge inverter, without exceeding the limits onthe input current ripples.

FIG. 32 illustrates the startup voltages and currents when the 3 kWICM-controlled 3-phase inverter shown in FIG. 30 is connected to a low(p.f.=0.1) lagging power factor load in Δ configuration, with theapparent power of about 3 kW. Note that the transient current throughthe battery is bi-directional, going through the discharge-rechargecycles as needed, before the steady-state operation is achieved.

6 Bidirectionality of ICM-Controlled Inverters and AC/DC Converters

FIG. 33 provides an example of a single-phase III-bridge ICM-based AC/DCconverter with high power factor and low harmonic distortions.

As before, let us make a few sensible idealizations, including nearlyideal behavior of the controller circuit, insignificant voltage dropsacross the components of the bridge, negligible ohmic voltage dropsacross the reactive components, and constant inductances L and theoutput capacitance C_(out). We also assume a practical choice of theintegrator time constant T in the ICM controller circuit, and thehysteresis gap Δh of the Schmitt triggers, that ensures sufficientlyhigh switching frequencies for the switching ripples in the outputvoltage to be ignored. This also implies that we can consider aninstantaneous value of V_(AC) within a switching cycle to be effectivelyequal to the average value of V_(AC) over this cycle.

Note that rising and falling edges of an output of a Schmitt triggerhappen when its input crosses (effectively constant) respectivethresholds. Thus relating the inputs and the output of the integrator inthe ICM controller in FIG. 33, differentiating both sides, thenaveraging between a pair of rising or falling edges of either Q₁ or Q₂,would lead toV*=V _(AC) −βT{dot over (V)} _(AC).  (9)On the other hand, the line current I_(AC) in FIG. 33 may be related tothe line and switching voltages V_(AC) and V* according to the followingequation:

$\begin{matrix}{{{\overset{\_}{I}}_{AC} = {\frac{1}{2L}{\int{{dt}\left( {{\overset{\_}{V}}_{AC} - {\overset{\_}{V}}^{*}} \right)}}}},} & (10)\end{matrix}$and substituting V* from equation (9) into (10) would lead to

$\begin{matrix}{{{\overset{\_}{I}}_{AC} = {{\beta\frac{\tau}{2L}{\overset{\_}{V}}_{AC}} + {const}}},} & (11)\end{matrix}$where the constant of integration would be determined by the initialconditions and would decay to zero, due to the power dissipation in theconverter's components and the load, for a steady-state solution.

Thus in a steady state

${{\overset{\_}{I}}_{AC} = {{\beta\frac{\tau}{2L}{\overset{\_}{V}}_{AC}} \propto {\overset{\_}{V}}_{AC}}},$leading to AC/DC conversion with effectively unity power factor and lowharmonic distortions. Note that high power factor in the ICM-based AC/DCconverter shown in FIG. 33 is achieved without need for current sensing,and the PFC is entirely voltage-based.

The output parallel RC circuit forms a current filter which, withrespect to the input current fed by a current source, acts as a 1storder lowpass filter with the time constant τ_(out)=R_(load)C_(out), andthus, for sufficiently large τ_(out) (e.g. an order of magnitude largerthan ƒ_(AC) ⁻¹), the average value of the output voltage V_(out) wouldbe proportional to the RMS of the line voltage and may be expressed as

$\begin{matrix}{{\left\langle V_{out} \right\rangle = {{\left( {\eta\;\beta\; R_{load}\frac{\tau}{2L}} \right)^{\frac{1}{2}}\left\langle V_{AC}^{2} \right\rangle^{\frac{1}{2}}} = {K\left\langle V_{AC}^{2} \right\rangle^{\frac{1}{2}}}}},} & (12)\end{matrix}$where the angular brackets denote averaging over sufficiently large timeinterval (e.g. several AC cycles), η is the converter efficiency, andwhere

$\left\langle V_{AC}^{2} \right\rangle^{\frac{1}{2}}$is the RMS of the line voltage.

For example, for L=195 μH and T=13.7 μs, 2L/T≈28.5Ω. Thus for β=1 and95% efficiency R_(load)=120Ω would result in K≈2.

For regulation of the output voltage V_(out), the load conductance maybe obtained by sensing both the output voltage and the load currentI_(load), and the coefficient β may be adjusted and/or maintained to beproportional to the ratio I_(load)/V_(out).

For example, from equation (12),

$\begin{matrix}{\beta = {{\frac{2K^{2}L}{\eta\;\tau}R_{load}^{- 1}} = {\frac{2K^{2}L}{\eta\;\tau}\frac{I_{load}}{V_{out}}}}} & (13)\end{matrix}$would lead to the nominal AC/DC conversion ratio

${\left\langle V_{out} \right\rangle\text{/}\left\langle V_{AC}^{2} \right\rangle^{\frac{1}{2}}} = {K.}$

FIG. 34 illustrates the behavior of a particular implementation of a 2kW ICM-controlled single-phase AC/DC converter shown in FIG. 33. In thisexample, the load conductance switches (effectively instantaneously)between zero and the full load, and the coefficient β is obtainedaccording to equation (13). One should be able to see that, after theconverter is powered up (after the AC source is connected at t=2.75 ms)the output voltage converges to the value given by equation (12), andthe line current converges to the steady-state current given by equation(11) with const=0. The bottom panel in FIG. 34 shows the PSD of thesteady-state current at full load, illustrating that the switchingfrequency would span a continuous range of values.

Further, additional output voltage regulation based on the differencebetween the desired nominal (“reference”) and the actual (

V_(out)

) output voltages may be added. For example, a term proportional to saiddifference may be added to the parameter β.

7 Variations of ICM Controller Topologies and 3-Phase AC/DC and DC/ACConverters

One skilled in the art will recognize that ICM controller allows mappingof the voltage relations among the inputs and the outputs of theintegrators in the ICM controller into various desired voltage andcurrent relations in a converter.

For example, as illustrated in FIG. 35(a), given a plurality ofintegrator inputs and a plurality of comparator (Schmitt trigger) inputsadded, along with the integrator output, to the comparator (Schmitttrigger) input, these pluralities of inputs may be related by thefollowing differential equation:

$\begin{matrix}{{{\frac{1}{T}{\sum\left( \overset{\_}{{plurality}\mspace{14mu}{of}\mspace{14mu}{integrator}\mspace{14mu}{inputs}} \right)}} = {\frac{d}{dt}{\sum\left( \overset{\_}{{plurality}\mspace{14mu}{of}\mspace{14mu}{added}\mspace{14mu}{comparator}\mspace{14mu}{inputs}} \right)}}},} & (14)\end{matrix}$where the overlines denote averaging over a time interval between a pairof rising or falling edges of either first or second Schmitt trigger.Then (as illustrated, for example, in Sections 3.1 and 6) the desiredvoltage and current relations converter may be mapped (typically,through the relation to a switching voltage(s)) into the voltagerelations in an ICM controller.

Note that, in accordance with equation (14), the ICM controllers shownin FIGS. 35(b) and 35(c) would be effectively equivalent.

In FIG. 35(b) the integrator input signal comprises a first integratorinput component proportional to the switching voltage (μV*), a secondintegrator input component proportional to the AC source voltage(−μV_(AC)), and a third integrator input component proportional to atime derivative of said AC source voltage (βμτ{dot over (V)}_(AC), andthe Schmitt trigger input signal comprises a first Schmitt trigger inputcomponent proportional to said integrator output signal and an optionalsecond Schmitt trigger input component proportional to a frequencycontrol signal (V_(FCS)).

In FIG. 35(c) the integrator input signal comprises a first integratorinput component proportional to the switching voltage (μV*) and a secondintegrator input component proportional to the AC source voltage(−V_(AC)), and the Schmitt trigger input signal comprises a firstSchmitt trigger input component proportional to said integrator outputsignal, a second Schmitt trigger input component component proportionalto said AC source voltage (βμτV_(AC)/T), and an optional third Schmitttrigger input component proportional to a frequency control signal(V_(FCS)).

FIG. 36 provides an example of ICM-based control of a 3-phase AC/DCconverter with high power factor and low harmonic distortions. As oneshould be able to see in FIG. 36, the switches in the bridge arecontrolled by three instances of an controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

With β given by

$\begin{matrix}{{\beta = {\frac{K^{2}L}{3\eta\;\tau}\frac{I_{load}}{V_{out}}}},} & (15)\end{matrix}$where η is the converter efficiency, the nominal AC/DC conversion ratioof the 3-phase AC/DC converter shown in FIG. 36 would be

${{\left\langle V_{out} \right\rangle\text{/}\left\langle V_{LL}^{2} \right\rangle^{\frac{1}{2}}} = K},$where V_(LL) is the nominal line-to-line voltage. Further, additionaloutput voltage regulation based on the difference between the desirednominal (“reference”) and the actual (

V_(out)

) output voltages may be added. For example, a term proportional to saiddifference may be added to the parameter β.

Also, a desired voltage output V_(ref) may be achieved by using theparameter β that may be expressed as follows:

$\begin{matrix}{\beta = {\frac{3V_{ref}^{2}}{\left\langle V_{ab}^{2} \right\rangle + \left\langle V_{bc}^{2} \right\rangle + \left\langle V_{ca}^{2} \right\rangle}\frac{L}{\eta\;\tau}{\frac{I_{load}}{V_{out}}.}}} & (16)\end{matrix}$

Note that with the inputs to the integrators of the ICM controllers asshown in FIG. 36, any chosen single node of the power stage (e.g., V₊,V⁻, the “neutral” node V_(N), a switching node a, b, or c, or an AC nodeV_(a), V_(b), or V_(c)) may be grounded.

We may refer to the voltages V_(a)′=V_(a)−V_(N), V_(b)′=B_(b)−V_(N), andV_(c)′=V_(c)−V_(N) shown in FIG. 36 as line-to-neutral voltages of the3-phase source voltage. In practical implementations it would be commonthat the “neutral” node is grounded, i.e., V_(N)=0.

FIG. 37 illustrates the behavior of a particular implementation of a 6kW ICM-controlled 3-phase AC/DC converter shown in FIG. 36. In thisexample, the load conductance switches (effectively instantaneously)between 10% and the full load, and the coefficient β is obtainedaccording to equation (16).

Note that the ICM-based control of the converter shown in FIG. 36 wouldalso ensure that the difference between the common mode output voltageV_(CM)=(V₊+V⁻)/2 and the “neutral” node voltage V_(N) would be azero-mean voltage with the main frequency content at the switchingfrequencies. This is illustrated in panels (c) and (d) of FIG. 38, whichshow the PSDs of V_(CM)−V_(N) (with the “neutral” node grounded, i.e.,V_(N)=0) for the steady-state operation at full (panel (c)) and 10%(panel (d) of the nominal load for a particular implementation of a 6 kWICM-controlled 3-phase AC/DC converter shown in FIG. 36.

Panels (a) and (b) of FIG. 38 show the PSDs of the steady-state inductorcurrents at full and 10% loads, illustrating low harmonic distortionsand the fact that the switching frequency would span a continuous rangeof values.

FIG. 39 provides an example of ICM-based control of a 3-phase AC/DCconverter that is effectively equivalent to that shown in FIG. 36. Inthis example, an input signal of the integrator in an ICM controller isa linear combination of voltages proportional to (1) a line-to-linevoltage (e.g. −μV_(ab)), (2) its time derivative (e.g. βμτ{dot over(V)}_(ab)), and (3) the difference between two respective switchingvoltages (e.g. μV_(ab)*).

FIG. 40 provides an example of an ICM-controlled 3-phase inverter (DC/ACconverter). Here, the output line-to-line voltages V_(ab)=V_(a)−V_(b),V_(bc)=V_(b)−V_(c), and V_(ca)=V_(c)−V_(a) would be proportional to therespective differences between the reference voltages V_(a)−V_(b),V_(b)−V_(c), and V_(c)−V_(a), where V_(a)+V_(b)+V_(c)=0. Note that, ingeneral, the reference voltages do not need to be sinusoidal signals.

We may refer to the voltages V_(a)′=V_(a)−V_(N), V_(b)′=V_(b)−V_(N), andV_(c)′=V_(c)−V_(N) shown in FIG. 40 as line-to-neutral voltages of the3-phase output voltage. Note that in practical implementations the“neutral” node V_(N) may be floating (not grounded), and thus may be a“virtual neutral”. Whether the node V_(N) is grounded or not, we mayrefer to it as the “virtual neutral”.

We may also refer to the voltages V_(ab)=V_(a)−V_(b),V_(bc)=V_(b)−V_(c), and V_(ca)=V_(c)−V_(a), and the voltagesV_(a)′=V_(a)−V_(N), V_(b)′=V_(b)−V_(N), and V_(c)′=V_(c)−V_(N) shown inFIG. 40, as simply “AC voltages”.

Further note that the virtual neutral is connected to the AC outputs bycapacitors, and that the capacitances of these capacitors may or may notbe effectively equal.

As one should be able to see in FIG. 40, the switches in the bridge arecontrolled by three instances of an ICM controller disclosed herein, andeach leg of the bridge is separately controlled by its respective ICMcontroller.

Note that with the inputs to the integrators of the ICM controllers asshown in FIG. 40, the ground may be placed at (connected to) any chosensingle node of the power stage (e.g., V₊, V⁻, the “neutral” node V_(N),a switching node a, b, or c, or an AC node V_(a), V_(b), or V_(c)).

Also note that the inputs signals of the integrator in an ICM controllerin the inverter shown in FIG. 40 may also be as shown in FIG. 30. InFIG. 30, an input signal of the integrator in an ICM controller is alinear combination of voltages proportional to (1) a difference betweentwo switching voltages (e.g. μV_(ab)*), (2) the time derivative of therespective line-to-line voltage (e.g. μτ{dot over (V)}_(ab)), and (3)the respective reference voltage (e.g. V_(ab)).

FIG. 41 illustrates transient output power, voltages and currents, andthe inductor currents, for a particular implementation of a 6 kWICM-controlled 3-phase inverter shown in FIG. 40, in response tofull-range (and independent of each other) step changes in theline-to-line resistive loads.

8 Digital Implementations of ICM Controllers

While the ICM development relies on analog methodology, in manypractical deployments low computational cost field-programmable gatearray (FPGA) implementations may be a preferred choice, offeringon-the-fly control reconfigurability and resistance to on-boardelectromagnetic interference (EMI). However, to benefit from the analogconcept, a sampling rate in a digital ICM implementation would need tobe significantly higher (e.g. by two or more orders of magnitude) thanthe switching frequency.

Since the ICM algorithm does not use products/ratios of the inputs,and/or their nonlinear functions such as coordinate transformations,instead of using high-resolution analog-to-digital converters (ADCs),the desired “effectively analog” controller bandwidth may be easilyachieved by using simple 1-bit ΔΣ modulators [8, 9] (e.g., 1st order ΔΣmodulators), as illustrated in FIG. 42.

In the figure, the lowpass filter preceding the numerical Schmitttriggers may be an infinite impulse response (IIR) filter with thebandwidth of order of the typical switching frequency. An IIR filter(e.g. a 2nd order IIR lowpass Bessel filter) may be used in order toboth reduce the group delay and lower the computational and memoryrequirements. Provided that the sampling rate of the ΔΣ modulators issufficiently high, the performance of such a digital ICM controller maybe effectively equivalent to that of the respective analog controller,as illustrated in FIG. 43.

In FIGS. 42 and 43, a numerical integrator may compute a “numericalantiderivative” as follows: “IntOut(i)=IntOut (i−1)+IntIn(i)*dt” where“dt” is the sampling time interval.

A second order analog lowpass filter may be described by the followingdifferential equation:ζ(t)=z(t)−τ{dot over (ζ)}(t)−(τQ)²{umlaut over (ζ)}(t),  (17)where z(t) and ζ(t) are the input and the output signals, respectively,T is the time parameter of the filter (inversely proportional to thecorner frequency ƒ₀, τ≈1/(2πQƒ₀)), Q is the quality factor, and the dotand the double dot denote the first and the second time derivatives,respectively. For the Bessel filter, Q=1√{square root over (3)}.

When the signal sampling rate is sufficiently high (e.g. the samplinginterval is much smaller than the time parameter), a finite-differencesolution of equation (17) would sufficiently well approximate the analogfilter.

An example of such a numerical algorithm for a 2nd order IIR lowpassBessel filter may be given by the following MATLAB function:

function zeta = Bessel_2nd_order(z,dt,tau)  zeta = zeros(size(z)); zeta(1) = z(1);  T1sq = .5*dt*tau*sqrt(3);  T2sq = tau{circumflex over( )}2;  dtsq = dt{circumflex over ( )}2;  zeta(2) = ( 2*T2sq*zeta(1) +zeta(1)*(T1sq−T2sq) ) / (T2sq+T1sq);  for i = 3:length(z);   dZ = z(i-1)− zeta(i-1);   zeta(i) = ( dtsq*dZ + 2*T2sq*zeta(i-1) +zeta(i-2)*(T1sq−T2sq) ) / (T2sq+T1sq);  end return

In this example, “z” is the input signal, “zeta” is the output, “tau” isthe time parameter of the filter, and “dt” is the sampling interval.

An example of an algorithm for an inverting numerical Schmitt triggermay be given by the following MATLAB function:

function y = SchmittTriggerInv(x,h0,dh,y_old)  if x<h0, y = 1;  elseifx>h0+dh, y = 0;  else y = y_old;  end return

In this example, “x” is the input signal, “y” is the output, h⁰ is thelower threshold of the trigger, and “dh” is the hysteresis gap.

One skilled in the art will recognize from the above description that anICM controller may be implemented in a digital signal processingapparatus performing numerical functions that include numericalintegration function, lowpass filtering function, and numerical Schmitttrigger function.

One skilled in the art will also recognize that oversampled modulatorswith the amplitude resolution higher than 1 bit may be used to obtaindigital representations of the analog voltages for digital ICMcontrollers. For example, the quantizers in such modulators may berealized with N-level comparators, thus the modulators would have log₂(N)-bit outputs. A simple comparator with 2 levels would be a 1-bitquantizer; a 3-level quantizer may be called a “1.5-bit” quantizer; a4-level quantizer would be a 2-bit quantizer; a 5-level quantizer wouldbe a “2.5-bit” quantizer. A higher quantization level would allow for awider-bandwidth lowpass filtering.

Further, provided that the sampling rate of the ADCs is sufficientlyhigh, ADCs with even higher amplitude resolution (e.g. 6-bit or higher)may be used to obtain digital representations of the analog voltages fordigital ICM controllers. When the ADC amplitude resolution issufficiently high (e.g. 6-bit or higher), the lowpass filtering functionmay become optional, and only numerical integration function andnumerical Schmitt trigger function would be needed to implement adigital ICM controller. This is illustrated in FIG. 44 for 8-bit digitalrepresentations of the analog voltages.

9 Holistic Control of Three-Phase Bidirectional Rectifier

One skilled in the art will recognize from the description presented inthis disclosure that an analog (albeit permitting digitalimplementation) ICM controller may enable a minimalistic 6-switch bridgeto perform as a high-quality multi-level bidirectional three-phaserectifier, holistically incorporating startup, EMI, and overloadmanagement, tolerance to mains outage imbalance and/or phase loss, andoffering multiple ways to optimize the cost-size-weight-performancetradespace.

Voltage and current relations in a switching power converter would bebest described by a system of continuous-time differential equations,which may be easily solved, in real time, by a simple analog feedbackcircuit comprising an integrator. Under such a premise, the controllerbecomes a holistic part of the controller topology rather than acomputational add-on. Meeting additional specifications such aseffectively unity power factor (PF), low total harmonic distortion(THD), reliable regulation under a wide range of load conditions and/orchanges, tolerance to mains voltage imbalance and/or phase loss,startup, electromagnetic interference (EMI), and overload management,operation at variable AC frequencies, bidirectionality, and the abilityto connect converters in parallel to increase the output power and/orachieve N+1 redundancy may be innately incorporated into the controllerfunction.

For example, FIG. 45 shows the principal schematic of a 3-phase 6-switchrectifier that incorporates the power stage, EMI filtering (componentswithin the dashed-line boundary), and low-power analog circuitry thatprovides both the control of the power stage and non-dissipativeresonance damping of the EMI filters. As may be seen in FIG. 45, eachinstance of the ICM controller comprises (1) an integrator (with thetime constant T) and (2) two Schmitt triggers (inverting andnon-inverting, with the same hysteresis gap Δh) with a slight offset inthe reference voltage. Each ICM controller supplies a pair of the switchcontrol signals Q_(ij) to the MOSFET switches in the respective leg ofthe bridge.

For simplicity, let us first consider the operation of the convertershown in FIG. 45 without the EMI filtering (that is, without the circuitcomponents and the ICM integrator inputs outlined by the dashed-lineboundaries). In such a case, with a few sensible idealizations, the ICMcontrollers would solve a system of the following differentialequations:

$\begin{matrix}\left\{ {\begin{matrix}{{\overset{\_}{I}}_{a} = {{\beta\frac{\tau}{L}{\overset{\_}{V}}_{a}^{\prime}} - {\frac{1}{L}{\int{{dt}\left( {{\overset{\_}{V}}_{CM} - {\overset{\_}{V}}_{N}} \right)}}}}} \\{{\overset{\_}{I}}_{b} = {{\beta\frac{\tau}{L}{\overset{\_}{V}}_{b}^{\prime}} - {\frac{1}{L}{\int{{dt}\left( {{\overset{\_}{V}}_{CM} - {\overset{\_}{V}}_{N}} \right)}}}}} \\{{\overset{\_}{I}}_{c} = {{\beta\frac{\tau}{L}{\overset{\_}{V}}_{c}^{\prime}} - {\frac{1}{L}{\int{{dt}\left( {{\overset{\_}{V}}_{CM} - {\overset{\_}{V}}_{N}} \right)}}}}} \\{{I_{a} + I_{b} + I_{c}} = 0}\end{matrix},} \right. & (18)\end{matrix}$where overlines denote averaging over a time interval between any pairof rising/falling edges of the respective switch control signals Q_(ij).It should be easily seen that, for a balanced system, a steady-statesolution of (18) would lead to proportionality between the line voltagesand the respective currents, providing 3-phase AC/DC conversion with anearly unity power factor and low harmonic distortions. Note that theswitching behavior of the ICM-based converter shown in FIG. 45 may notbe characterized in such simple terms as pulse-width or pulse-frequencymodulation (PWM or PFM), and that the voltage at a switching node (e.g.V_(a)*−V_(N)) would exhibit an interleaved 5-level, intrinsicallyspread-spectrum pattern (see, e.g., FIG. 49) with a frequency rangedetermined by the AC and DC voltages and the values of the parameters μ,T, and Δh (and, when operating in a discontinuous conduction mode atlight loads, by the load). Also note that in the configuration shown inFIG. 45 the difference between the common mode output voltageV_(CM)=(V₊+V⁻)/2 and the “neutral” node voltage V_(N) would be azero-mean voltage with the main frequency content at the switchingfrequencies. Further, when the LC EMI filtering network is added, theadditional ICM controller inputs (outlined by the dashed-lineboundaries, α˜√{square root over (LC)}/τ) would provide non-dissipativeresonance damping of the LC circuits in the EMI filters.

We may refer to the voltages V′_(a), V′_(b), and V′_(c) indicated inFIG. 45 as “AC voltages”, or as “AC line voltages”. We may further referto the voltages {tilde over (V)}′_(a), {tilde over (V)}′_(b), and {tildeover (V)}′_(c) indicated in FIG. 45 as “LC filter voltages”, or “LCdamping voltages”.

One skilled in the art will recognize that a variety of LC dampingvoltages different from those shown in FIG. 45 may be constructed toprovide resonance damping of the LC circuits in the EMI filters. Forexample, the LC damping voltages may be obtained as a combination (e.g.a linear combination) of other node voltages of the LC circuits in theEMI filters.

As follows from equation (18), the steady-state AC power drawn from (orsupplied to for β<0) the 3-phase AC source would be

$P_{AC} = {\beta\frac{\tau}{L}{\left( {\left\langle V_{a}^{\prime 2} \right\rangle + \left\langle V_{b}^{\prime 2} \right\rangle + \left\langle V_{c}^{\prime 2} \right\rangle} \right).}}$Then a desired regulated voltage output V_(ref) may be achieved by usingthe parameter β that may be expressed, for example, as

$\begin{matrix}{{\beta = {\frac{V_{ref}^{2}}{\left\langle V_{a}^{\prime 2} \right\rangle + \left\langle V_{b}^{\prime 2} \right\rangle + \left\langle V_{c}^{\prime 2} \right\rangle}\frac{L}{\eta\;\tau}\frac{I_{load}}{V_{DC}}}},} & (19)\end{matrix}$where η is the converter efficiency, and only the DC-side currentmeasurement may required for such voltage regulation. Equation (19) mayprovide the basis for voltage regulation of the ICM-based rectifier, andmay be modified in various ways to meet the desired specifications (e.g.the right-hand side of (19) may be multiplied by a positive power ofV_(ref)/V_(DC) to tighten the voltage regulation). For example, it maybe adjusted to adapt to severe mains voltage imbalance and/or phase loss(e.g., by replacing

V′_(a) ²

+

′_(b) ²

+(

V′_(c) ²

with (

V′_(a) ²

+

V′_(b) ²

)/2 for loss of V_(c)), and managing the inrush startup and the overloadcurrents may be achieved by limiting the maximum value of β. Further,changing the sign of β from positive to negative would reverse the powerflow, converting a rectifier into an inverter.

FIGS. 46 through 49 provide several examples of behavior and performanceof a particular implementation of an ICM-based 3-phase rectifier shownin FIG. 45, for 115 VAC to 400 VDC conversion with ƒ_(AC)=500 Hz. Fullyanalog ICM controller implementation was used to enable LTspicesimulations, and analog behavioral models (ABMs) were used to producethe ICM control signals. High-fidelity LTspice models for the SiCMOSFETs (C2M0025120D) and the SiC Schottky diodes (C4D20120A) were usedin the simulations, and, for efficiency/losses breakdown, simplifiedinductor losses assessment was used, that generally overestimates themagnetics losses as compared with those for carefully designedinductors.

FIG. 46 shows transient responses under mains voltage imbalance, FIG. 47provides the efficiency/losses breakdown, PF, and THD, FIG. 48 shows theFFTs of the steady-state line currents and CM/DM voltages at 10 kWoutput, and FIG. 49 shows the steady-state switching voltages at 10 kWoutput.

For given rectifier components and their values, the power losses invarious components would be different nonlinear functions of the load,and would also exhibit different nonlinear dependences on the integratortime constant T and/or the hysteresis gap Δh. Thus, given a particularchoice of the switches (e.g. particular MOSFET switches) and theirdrivers, the magnetics, and other passive rectifier components, byadjusting T and/or Δh one may achieve the best overall compromise amongvarious component power losses (e.g., between the bridge and theinductor losses), while remaining within other constraints on therectifier specifications. A digital ICM controller implementation wouldenable efficiency calibration (and/or “on-the-fly” adjustment) of therectifier by adjusting T and/or Δh based on the output power (orcurrent)) to maximize the efficiency for a given load.

9.1 Load/Power Sharing

A plurality of ICM-controlled rectifiers may be connected in parallel,for load/power sharing, e.g. to increase the output power and/or achieveN+1 redundancy.

For example, when N rectifiers are connected to a common AC source,regulation of the voltage output may be achieved by using the parameterβ for each ith rectifier that may be expressed, for example, as

$\begin{matrix}{{\beta_{i} = {p_{i}\frac{L_{i}}{\eta_{i}\tau_{i}}\frac{I_{load}}{V_{DC}}\frac{V_{ref}^{2}}{\left\langle V_{a}^{\prime 2} \right\rangle + \left\langle V_{b}^{\prime 2} \right\rangle + \left\langle V_{c}^{\prime 2} \right\rangle}}},} & (20)\end{matrix}$where the index i indicates the quantities for the ith rectifier, andp_(i) is the designated fractional power output of the ith rectifier,Σ_(i) ^(N)=1.

Additional ICM controller inputs (e.g. indicative of linear combinationsof node voltages) may be used to ensure the desired coordinatedperformance of load sharing rectifiers, for example, to reduce theirstartup transients.

10 ICM-Based H-Bridge Converters with 3-Level Switching

The basic “free-running” H-bridge converter (see, e.g., FIGS. 14 and 33)with a single ICM controller is a two-level converter, wherein theswitching voltage V* effectively alternates between the two voltagelevels ±V_(in). As follows from the detailed description given above,however, ICM controllers may allow us to achieve three-level switchingin an H-bridge converter, when the switching voltage V* mostlyalternates either between zero and V_(in), or between zero and −V_(in).

Such 3-level switching may be highly desirable as it would improve theconverter performance (e.g. reduce THD and EMI) and/or its otherspecifications. For example, for the same inductor current ripplespecifications, we may reduce the size of the inductors and/or reducethe switching frequency. Or, for given inductors, we may reduce both theinductor current ripples and/or the switching frequency.

Three-level switching in an ICM-based H-bridge converter may be achievedby controlling each “leg” of the full H bridge by its own instance of anICM controller, and providing appropriate control signals to each of theICM controllers. This is illustrated in FIG. 50 for an H-bridgeinverter. By using the inputs to the integrators of the ICM controllersas shown in the figure, the 3-level switching would be enabled.

We may refer to the voltages V′₁=V₁−V_(N) and V′₂=V₂−V_(N) indicated inFIG. 50 as “AC line voltages”. While FIG. 50 shows, as an example, aparticular choice of switching and AC line voltages used as controllerinputs, one skilled in the art will recognize that differentcombinations (e.g. linear combinations) of switching and AC linevoltages may be used to achieve a desired switching pattern (e.g. athree-level switching pattern).

FIG. 51 illustrates performance of a 3-level ICM-controlled H-bridgeinverter in comparison with a respective 2-level inverter with the samepower stage components. One may see from the figure that the 3-levelcontrol reduces the inductor current ripples, EMI, and THD, whilemaintaining effectively the same range of switching frequencies.

One skilled in the art will recognize that an LC EMI filtering networkmay be added to an H-bridge converter in a manner similar to thatdepicted in FIG. 45 for a 3-phase converter. Further, LC dampingvoltages may be added as ICM controller inputs to provide resonancedamping of the LC circuits in the EMI filters.

11 “Grid Forming” and “Grid Following” Operation of ICM-Based H-BridgeSwitching Power Converters

The simulated examples in this section were performed in LTspice, andthus fully analog ICM controller implementation was used to enable theLTspice simulations. Analog Behavioral Models (ABMs) were used toproduce the ICM control signals. The 3-level modification of anICM-based H-bridge converter illustrated in FIG. 52 was used.

As shown in FIG. 52, the two “legs” of the full H bridge are eachcontrolled by its own instance of an ICM controller. In the “bare”implementation, the input to the ith ICM controller may consist of threevoltages: (1) the switching voltage V_(i)*′ proportional to the voltageat the switching node of the leg (this input would be the same for boththe grid forming and the grid following modes of operation), (2) the “ACsetting voltage” V_(i,set) (proportional to the grid voltage V_(i)′ forthe grid following mode, and to the “desired” reference voltage V_(ref)for the grid forming mode), and (3) the “power setting voltage” βV_(i)′.The coefficient β would be a positive constant for the grid formingmode, and would be a parameter (time-varying in general) proportional toa desired average “true” power drawn from (for β<0) and/or delivered to(for β>0) the grid while operating in the grid following mode.

An additional 4th (effectively the same for both the grid forming andthe grid following modes of operation) ICM control voltage (an LCdamping voltage) may be used when common mode (CM) and differential mode(DM) EMI filtering is added to the “bare” converter, to performnon-dissipative resonance damping of the CM and DM LC filters. Suchadditional EMI filtering would also improve the overall performance ofthe converters (including, e.g., improving PF at light loads andreducing THD).

In the grid forming mode of operation, an ICM-based II-bridge converterwould effectively serve as an AC voltage source, providing an AC outputvoltage proportional to the “desired” reference voltage V_(ref). In thegrid following mode, the converter would either supply (for β>0) aneffectively unity power factor (PF) AC power at set level

P_(AC)

∝ β (e.g. at optimal power point from a photovoltaic (PV) DC source), ordraw (for β<0) AC power at set level

P_(AC)

∝−β (with p.f.≈1) from the grid (e.g. to provide DC current for charginga battery).

Multiple ICM-based H-bridge converters may be directly connected inparallel (e.g., without a need for isolation transformers) to form amicrogrid, and the microgrid may further be connected to the main grid.

When connected to the main grid (that would be considered an AC voltagesource), all converters in the microgrid would operate in a gridfollowing mode, supplying to and/or drawing power from the main grid atset (and possibly time varying) power levels. In an islanded mode (whendisconnected from the main grid), one of the converters would operate ina grid forming mode, while the rest would operate in grid followingmodes. The designation of the grid forming converter would depend on theavailable and/or desired supply/demand power levels of each converter(e.g. depending on the AC load and/or charging battery states and/oroptimal power points of PV and/or other sources), and may change (e.g.using a hysteretic algorithm) as those power levels change in time.

It may be useful to think of a grid following converter with p.f.≈1 ashaving an average conductance

G′

≈−

P_(AC)

/(

V_(AC) ²

(positive when the power is drawn from the grid, and negative when thepower is supplied to the grid) to calculate the impedance of themicrogrid as seen by the grid forming converter.

One of the main appealing features of the ICM-based converters may betheir stability and effectively instantaneous (in comparison with the ACperiod) synchronization with the grid (for the grid following mode)and/or the reference voltage (for the grid forming mode), e.g.,accomplished on the order of tens of microseconds when switching betweenthe two modes.

In the illustrative setup shown in FIG. 53, two paralleled ICM-based Hbridge converters (assumed, e.g., to be powered by a 450 VDC battery anda 450 VDC PV DC sources) provide AC power to a highly nonlinear loadthat consists of a series RL circuit with p.f.=0.5 at 50 Hz (79.4 mHinductor in series with 14.4Ω resistor) in parallel with a full-wavediode rectifier. With no load at the output of the rectifier, thePV-based converter operates in the grid forming mode (at 50 Hz), and thebattery-based converter operates in a grid following mode (charging thebattery). With a heavy rectifier load, the PV-based converter operatesin a grid following mode, providing a set amount of average power (e.g.,determined by the optimal power point of the PV source), while thebattery-based converter supplements the rest of the power to the load,operating in the grid forming mode (at 60 Hz).

The grid setting voltages V_(ref) of the converters are chosen toproduce the same RMS output voltage 240 VAC, but are intentionally notsynchronized to each other and have different frequencies (50 Hz and 60Hz, respectively, for the PV- and battery-powered converter), toillustrate effectively instantaneous synchronization with the microgridand/or the reference voltage.

With a heavy load, the rectifier dissipates approximately 2 kW, and atno load its dissipation is negligible. At 50 Hz 240 VAC, the RL circuitdissipates approximately 1 kW, and at 60 Hz 240 VAC it dissipatesapproximately 750 W. Together, at 60 Hz 240 VAC the RL circuit and therectifier with the heavy load dissipate approximately 2.75 kW.

The optimal power point of the PV source was set at approximately 2 kW,leading to the (negative) conductance of the PV-based converteroperating in a grid following mode, as seen by the grid, ofapproximately −0.0347Ω⁻¹ (−28.8Ω). The charging power of the battery wasset at approximately 400 W (≈900 mA charging current), leading to theconductance of the battery-based converter operating in a grid followingmode, as seen by the grid, of approximately 0.0069Ω⁻¹ (144Ω).

FIG. 54 shows the DC voltages V_(DC) and V′_(DC), the DC powers(P_(DC)=I_(DC)V_(DC) and P′_(DC)=I′_(DC)V′_(DC)), the output (load)voltage V_(AC) and current I_(load), and the output voltage of therectifier V_(rec) for the setup of FIG. 53.

As should be easily seen in FIG. 54, the output AC voltage is maintainedaccording to that set by a grid forming converter, while the powersharing between the converters changes depending on the load. Note thatthe output AC voltage is well maintained even for a highly nonlinearrelation between the AC voltage and the load current (i.e. a heavyrectifier load).

With no load at the output of the rectifier, the PV-based converteroperates in a grid forming mode, supplying approximately 1 kW to the RLcircuit, and approximately 400 W for charging the battery (1.4 kWtotal). With a heavy rectifier load, the PV-based converter operates ina grid following mode, supplying approximately 2 kW, and thebattery-based converter operates in a grid forming mode, supplementingapproximately 750 W to the load (2.75 kW total).

12 Grid Forming and Grid Following Operation of ICM-Based 3-PhaseSwitching Power Converters

Multiple ICM-based 3-phase converters may also be directly connected inparallel (e.g., without a need for isolation transformers) to form amicrogrid, and the microgrid may further be connected to the main grid.

The three “legs” of the 6-switch bridge would be each controlled by itsown instance of an ICM controller. In the “bare” implementation, theinput to an ICM controller would consist of three voltages: (1) theswitching voltage V_(i)*′ proportional to the voltage at the ithswitching node of the leg (this input would be the same for both thegrid forming and the grid following modes of operation), (2) the “ACsetting voltage” V_(i,set) (proportional to the respective grid voltageV′_(i,AC) for the grid following mode, and to the “desired” referencevoltage V_(i,ref) for the grid forming mode), and (3) the “power settingvoltage” βV′_(i,AC). The coefficient β would be a positive constant forthe grid forming mode, and would be a parameter (time-varying ingeneral) proportional to a desired average “true” power drawn from (forβ<0) and/or delivered to (for β>0) the grid while operating in the gridfollowing mode.

An additional 4th (effectively the same for both the grid forming andthe grid following modes of operation) ICM control voltage (an LCdamping voltage) may be used when common mode (CM) and differential mode(DM) EMI filtering is added to the “bare” converter, to performnon-dissipative resonance damping of the CM and DM LC filters. Suchadditional EMI filtering would also improve the overall performance ofthe converters (including improving PF at light loads and reducing THD).

In the grid forming mode of operation, an ICM-based 6-switch 3-phaseconverter would effectively serve as a 3-phase AC voltage source,providing a 3-phase AC output voltage proportional to the “desired”reference voltage {V_(1,ref), V_(2,ref), V_(3,ref)}. In the gridfollowing mode, the converter would either supply (for β>0) aneffectively unity power factor (PF) AC power at set level

P_(AC)

∝ β (e.g. at optimal power point from a photovoltaic (PV) DC source), ordraw (for β<0) AC power at set level

P_(AC)

∝−β (with p.f.≈1) from the grid (e.g. to provide DC current for charginga battery).

When connected to the main grid (that would be considered a 3-phase ACvoltage source), all converters in the microgrid would operate in a gridfollowing mode, supplying to drawing power from the main grid at set(and possibly time varying) power levels. In an islanded mode (whendisconnected from the main grid), one of the converters would operate ina grid forming mode, while the rest would operate in grid followingmodes. The designation of the grid forming converter would depend on theavailable and/or desired supply/demand power levels of each converter(e.g. depending on the AC load and/or charging battery states and/oroptimal power points of PV and/or other sources), and may change (e.g.using a hysteretic algorithm) as those power levels change in time.

REFERENCES

-   [1] Qing-Chang Zhong and T. Hornik. Control of Power Inverters in    Renewable Energy and Smart Grid Integration. Wiley, 2013.-   [2] R. Bracewell. The Fourier Transform and Its Applications,    chapter “Heaviside's Unit Step Function, H(x)”, pages 61-65.    McGraw-Hill, New York, 3rd edition, 2000.-   [3] P. A. M. Dirac. The Principles of Quantum Mechanics. Oxford    University Press, London 4th edition, 1958.-   [4] A. V. Nikitin, “Method and apparatus for control of    switched-mode power supplies.” U.S. Pat. No. 9,130,455 (8 Oct.    2015).-   [5] A. V. Nikitin, “Switched-mode power supply controller.” U.S.    Pat. No. 9,467,046 (11 Oct. 2016).-   [6] “Little box challenge,” 26 Mar. 2016. [Online] Available:    https://en.wikipedia.org/wiki/Little_Box_Challenge-   [7] “Detailed inverter specifications, testing procedure, and    technical approach and testing application requirements for the    little box challenge,” 16 Jul. 2015. [Online]. Available:    https://www.littleboxchallenge.com/pdf/LBC-InverterRequirements-20150717.pdf-   [8] G. I. Bourdopoulos, A. Pnevmatikakis, V. Anastassopoulos,    and T. L. Deliyannis. Delta-Sigma Modulators: Modeling, Design and    Applications. Imperial College Press, London, 2003.-   [9] Y. Geerts, M. Steyaert, and W. M. C. Sansen. Design of Multi-Bit    Delta-Sigma A/D Converters. The Springer International Series in    Engineering and Computer Science. Springer US, 2006.

Regarding the invention being thus described, it will be obvious thatthe same may be varied in many ways. Such variations are not to beregarded as a departure from the spirit and scope of the invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the claims. It is to beunderstood that while certain now preferred forms of this invention havebeen illustrated and described, it is not limited thereto except insofaras such limitations are included in the following claims.

I claim:
 1. A switching converter capable of converting a 3-phase ACsource voltage into a DC output voltage and providing a DC power output,wherein said 3-phase AC source voltage is characterized by three ACvoltages, wherein an AC voltage is one of said three AC voltages,wherein said DC output voltage is characterized by a DC common modevoltage, wherein said switching converter comprises a 3-phase bridgecomprising three pairs of switches and capable of providing threeswitching voltages, wherein a switching voltage is provided by a pair ofswitches controlled by a controller providing a 1st control signal and a2nd control signal, and wherein a 1st switch of said pair of switches iscontrolled by said 1st control signal and a 2nd switch of said pair ofswitches is controlled by said 2nd control signal, said switchingconverter further comprising a digital signal processing apparatusperforming numerical functions including: a) a numerical integratorfunction operable to receive an integrator input and to produce anintegrator output, wherein said integrator output is proportional to anumerical antiderivative of said integrator input; b) a 1st numericalSchmitt trigger characterized by a hysteresis gap and a 1st referencelevel, and operable to receive a Schmitt trigger input and to producesaid 1st control signal; and c) a 2nd numerical Schmitt triggercharacterized by said hysteresis gap and a 2nd reference level, andoperable to receive said Schmitt trigger input and to produce said 2ndcontrol signal; wherein said integrator input comprises a sum of adigital representation of said AC voltage and a digital representationof the difference between said switching voltage and said DC common modevoltage, and wherein said Schmitt trigger input comprises saidintegrator output.
 2. The switching converter of claim 1 wherein said DCoutput voltage is characterized by a desired DC voltage value, whereinsaid Schmitt trigger input further comprises a component proportional tosaid digital representation of said AC voltage, and wherein themagnitude of said component proportional to said digital representationof said AC voltage is chosen to provide said desired DC voltage value.3. The switching converter of claim 1 wherein said DC power output ischaracterized by a desired DC power value, wherein said Schmitt triggerinput further comprises a component proportional to said digitalrepresentation of said AC voltage, and wherein the magnitude of saidcomponent proportional to said digital representation of said AC voltageis chosen to provide said desired DC power value.
 4. The switchingconverter of claim 1 further comprising an LC EMI filtering network,wherein said Schmitt trigger input further comprises a componentproportional to a digital representation of an LC damping voltage, andwherein said LC damping voltage is chosen to provide resonance dampingof said LC EMI filtering network.
 5. A switching converter capable ofconverting a DC source voltage into a 3-phase AC output voltage andproviding an AC power output, wherein said 3-phase AC output voltage ischaracterized by three AC voltages indicative of respective AC settingvoltages, wherein an AC voltage is one of said three AC voltages,wherein said DC source voltage is characterized by a DC common modevoltage, wherein said switching converter comprises a 3-phase bridgecomprising three pairs of switches and capable of providing threeswitching voltages, wherein a switching voltage is provided by a pair ofswitches controlled by a controller providing a 1st control signal and a2nd control signal, and wherein a 1st switch of said pair of switches iscontrolled by said 1st control signal and a 2nd switch of said pair ofswitches is controlled by said 2nd control signal, said switchingconverter further comprising a digital signal processing apparatusperforming numerical functions including: a) a numerical integratorfunction operable to receive an integrator input and to produce anintegrator output, wherein said integrator output is proportional to anumerical antiderivative of said integrator input; b) a 1st numericalSchmitt trigger characterized by a hysteresis gap and a 1st referencelevel, and operable to receive a Schmitt trigger input and to producesaid 1st control signal; and c) a 2nd numerical Schmitt triggercharacterized by said hysteresis gap and a 2nd reference level, andoperable to receive said Schmitt trigger input and to produce said 2ndcontrol signal; wherein said integrator input comprises a sum of adigital representation of said AC setting voltage and a digitalrepresentation of the difference between said switching voltage and saidDC common mode voltage, and wherein said Schmitt trigger input comprisessaid integrator output.
 6. The switching converter of claim 5 whereinsaid AC voltage is characterized by a desired AC voltage and whereinsaid AC setting voltage is proportional to said desired AC voltage. 7.The switching converter of claim 5 wherein said AC power output ischaracterized by a desired AC power output, wherein said AC settingvoltage is proportional to said AC voltage, wherein said Schmitt triggerinput further comprises a component proportional to a digitalrepresentation of said AC voltage, and wherein the magnitude of saidcomponent proportional to said digital representation of said AC voltageis chosen to provide said desired AC power output.
 8. The switchingconverter of claim 5 further comprising an LC EMI filtering network,wherein said Schmitt trigger input further comprises a componentproportional to a digital representation of an LC damping voltage, andwherein said LC damping voltage is chosen to provide resonance dampingof said LC EMI filtering network.
 9. An AC/DC converter capable ofconverting an AC source voltage into a DC output voltage and providing aDC power output, wherein said DC output voltage is characterized by a DCcommon mode voltage, wherein said AC source voltage is characterized bytwo AC line voltages, wherein an AC voltage is one of said two AC linevoltages, wherein said AC/DC converter comprises an H bridge comprisingtwo pairs of switches and capable of providing two switching voltages,wherein a switching voltage is provided by a pair of switches controlledby a controller providing a 1st control signal and a 2nd control signal,and wherein a 1st switch of said pair of switches is controlled by said1st control signal and a 2nd switch of said pair of switches iscontrolled by said 2nd control signal, said switching converter furthercomprising a digital signal processing apparatus performing numericalfunctions including: a) a numerical integrator function operable toreceive an integrator input and to produce an integrator output, whereinsaid integrator output is proportional to a numerical antiderivative ofsaid integrator input; b) a 1st numerical Schmitt trigger characterizedby a hysteresis gap and a 1st reference level, and operable to receive aSchmitt trigger input and to produce said 1st control signal; and c) a2nd numerical Schmitt trigger characterized by said hysteresis gap and a2nd reference level, and operable to receive said Schmitt trigger inputand to produce said 2nd control signal; wherein said integrator inputcomprises a sum of a digital representation of said AC voltage and adigital representation of the difference between said switching voltageand said DC common mode voltage, and wherein said Schmitt trigger inputcomprises said integrator output.
 10. The AC/DC converter of claim 9wherein said DC output voltage is characterized by a desired DC voltagevalue, wherein said Schmitt trigger input further comprises a componentproportional to said digital representation of said AC voltage, andwherein the magnitude of said component proportional to said digitalrepresentation of said AC voltage is chosen to provide said desired DCvoltage value.
 11. The AC/DC converter of claim 9 wherein said DC poweroutput is characterized by a desired DC power value, wherein saidSchmitt trigger input further comprises a component proportional to saiddigital representation of said AC voltage, and wherein the magnitude ofsaid component proportional to said digital representation of said ACvoltage is chosen to provide said desired DC power value.
 12. Theswitching converter of claim 9 further comprising an LC EMI filteringnetwork, wherein said Schmitt trigger input further comprises acomponent proportional to a digital representation of an LC dampingvoltage, and wherein said LC damping voltage is chosen to provideresonance damping of said LC EMI filtering network.
 13. A DC/ACconverter capable of converting a DC source voltage into an AC outputvoltage and providing an AC power output, wherein said AC output voltageis characterized by two AC line voltages indicative of respective ACsetting voltages, wherein an AC voltage is one of said two AC voltages,wherein said DC source voltage is characterized by a DC common modevoltage, wherein said DC/AC converter comprises an H bridge comprisingtwo pairs of switches and capable of providing two switching voltages,wherein a switching voltage is provided by a pair of switches controlledby a controller providing a 1st control signal and a 2nd control signal,and wherein a 1st switch of said pair of switches is controlled by said1st control signal and a 2nd switch of said pair of switches iscontrolled by said 2nd control signal, said switching converter furthercomprising a digital signal processing apparatus performing numericalfunctions including: a) a numerical integrator function operable toreceive an integrator input and to produce an integrator output, whereinsaid integrator output is proportional to a numerical antiderivative ofsaid integrator input; b) a 1st numerical Schmitt trigger characterizedby a hysteresis gap and a 1st reference level, and operable to receive aSchmitt trigger input and to produce said 1st control signal; and c) a2nd numerical Schmitt trigger characterized by said hysteresis gap and a2nd reference level, and operable to receive said Schmitt trigger inputand to produce said 2nd control signal; wherein said integrator inputcomprises a sum of a digital representation of said AC setting voltageand a digital representation of the difference between said switchingvoltage and said DC common mode voltage, and wherein said Schmitttrigger input comprises said integrator output.
 14. The switchingconverter of claim 13 wherein said AC voltage is characterized by adesired AC voltage and wherein said AC setting voltage is proportionalto said desired AC voltage.
 15. The switching converter of claim 13wherein said AC power output is characterized by a desired AC poweroutput, wherein said AC setting voltage is proportional to said ACvoltage, wherein said Schmitt trigger input further comprises acomponent proportional to a digital representation of said AC voltage,and wherein the magnitude of said component proportional to said digitalrepresentation of said AC voltage is chosen to provide said desired ACpower output.
 16. The switching converter of claim 13 further comprisingan LC EMI filtering network, wherein said Schmitt trigger input furthercomprises a component proportional to a digital representation of an LCdamping voltage, and wherein said LC damping voltage is chosen toprovide resonance damping of said LC EMI filtering network.